The present invention relates generally to analog optical processing, and more particularly to an analog optical processor for performing affine transformations and constructing fractal objects.
An affine transformation is a mathematical transformation equivalent to a rotation, translation, and contraction (or expansion) with respect to a fixed origin and coordinate system. In computer graphics, affine transformations can be used to generate fractal objects which have significant potential for modeling natural objects, such as trees, mountains and the like.
A set of affine transformations together with an associated set of probabilities form an Iterated Function System ("IFS") that can generate a fractal object. Each IFS comprises a set of affine transformations and an associated set of probabilities. See, e.g., L. Demko et al., "Construction of Fractal Objects with Iterated Function Systems," Computer Graphics, Vol. 19(3), pages 271-278 (July, 1985) SIGGRAPH '85 Proceedings. Presently, to find an IFS for a given object to be modeled, scientists must try many transformation functions. For each set of functions, millions of affine transformations will have to be done. It requires a great deal of time and money to do this with digital computers. Researchers have been using trial-and-error methods to find an IFS for an object to be modeled because no systematic method is known to exist.
It is therefore a primary objective of the present invention to provide a faster means of performing a great number of affine transformations, thus enabling a faster construction of fractal objects with Iterated Function Systems.
Another objective of the present invention is to provide an analog optical processing procedure instead of a digital processing procedure for performing affine transformations and constructing fractal objects.
Another objective of the present invention is to provide an analog optical processing procedure including elements to perform probability functions, and thus to comprise an optical IFS.
Another objective of the present invention is to provide an optical processor providing the advantages of high speed and parallelism to speed up the trial-and-error process of discovering a desired IFS.